Impact of the electrolyte initial pH values

Chapter V: Numerical simulation of hydrogen gas evolution on planar

5.3 Results and Discussion

5.3.6 Impact of the electrolyte initial pH values

in terms of increasing solution conductance with higher nominal current densities. When the nominal current density increases from 100 mA cm^-2 to 150 mA cm^-2, the dissolved H2

concentration on the top end of the microwires increases by 12 mM accordingly, which results in 3 mV of 𝜂𝜂𝐶𝐶 increase. On the other hand, with the planar electrode, the dissolved H2 concentration at the electrode-electrolyte interface reduces from 33.76 mM to 33.42 mM.

The dissolved H2 accumulates even more rest part of the microwire electrodes. The reason for this great accumulation is that with surface cavity radius of 4 µm and under the nominal current density of 150 mA cm^-2, for the µW 6 | 14 configuration, the bubble break-off diameter is 102 µm, while for the planar electrode, the bubble break-off diameter is only 48 µm, which leads to a much higher mass transfer rate of hydrogen from the liquid phase to the gas phase and much less accumulation of dissolved hydrogen at the electrode-electrolyte interface.

Figure 5.10 For the planar electrode system with the same nominal current density, the bubble related ohmic drop linearly decreases with the increasing initial sulfuric acid concentration.

Therefore, under the same current density, the ohmic drop in the solution turns out to be higher with lower initial sulfuric acid concentration. As Figure 5.10 shows, for the planar electrode system with the same nominal current density, the bubble related ohmic drop linearly decreases with the increasing initial sulfuric acid concentration. Besides, with the same boundary layer thickness, the limiting current density will also linearly decrease with the reducing sulfuric acid concentration. For example, with the boundary layer thickness of 100 µm, the limiting current density is 159 mA cm^-2 for 0.5 M sulfuric acid, while 318 mA cm^-2 for 1 M sulfuric acid.

5.4 Conclusions

The bubble related ohmic drop within the solution increase with the nominal current density and flatness of the electrode surface. With the surface cavity radius of 20 µm, even the nominal current density reaches 300 mA cm^-2, the bubble associated ohmic drop, ∆𝐸𝐸_{𝑜𝑜ℎ𝑚𝑚}^′ , is not playing an important role in terms of the total bubble related potential drop increase in the cathodic chamber. But when the surface cavity radius is reduced to 4 µm, under nominal current density larger than 200 mA cm^-2, ∆𝐸𝐸_{𝑜𝑜ℎ𝑚𝑚}^′ is equivalent to at least 10% of 𝜂𝜂_{𝑆𝑆𝑟𝑟𝑒𝑒𝑒𝑒𝑜𝑜} due to the increased bubble vol. fraction and reduced conductance within the solution. The decrease of initial sulfuric acid concentration would cause an increase in ∆𝐸𝐸_{𝑜𝑜ℎ𝑚𝑚}^′ and the solution conductance is proportional to the initial electrolyte concentration. The local reversible hydrogen electrode potential can be shifted by accumulations of dissolved H2 at the electrode-electrolyte interface, which contributes the most in terms of the bubble associated potential drop between the cathode and reference electrode. When the electrode surface is relatively flat with the cavity radius equal to 4 µm, the local reversible hydrogen electrode potential shift due to existing bubbles, 𝜂𝜂_𝐶𝐶, decreases with the nominal current density due to the decreasing dissolved H2 concentration at the electrode-electrolyte interface. On the other hand, when the electrode surface is relatively rough with the cavity radius equal to 20 µm, the change of 𝜂𝜂_𝐶𝐶 doesn’t behave monotonously with the nominal current density. Under lower current densities, it goes up with the current density and reaches the peak at 250 mA cm^-2 for a planar electrode configuration then gradually decreases. It is

worth pointing out that with this kind of electrode surface roughness, the local reversible hydrogen electrode potential shift contributes at least 85% of the total bubble associated potential drop increase in the cathodic chamber. Bubbles adhering to the electrode surface will cause an additional overpotential increase, 𝜂𝜂ℎ. But based on the calculation, it is known that 𝜂𝜂_ℎ contributes less than 10% of the total bubble related potential drop increase in the cathodic chamber when the nominal current density is not greater than 300 mA cm^-2. ∆𝐸𝐸_{𝑜𝑜ℎ𝑚𝑚}^′ , 𝜂𝜂𝐶𝐶 and 𝜂𝜂ℎ makes up the total additional potential drop between the cathode and reference electrode due to existing bubbles. For a planar electrode configuration, the sum of these terms is comparable to the ideal overpotential, 𝜂𝜂𝑆𝑆𝑟𝑟𝑒𝑒𝑒𝑒𝑜𝑜, predicted for a planar Pt surface under the same current density, it equals to larger than 75% of 𝜂𝜂_{𝑆𝑆𝑟𝑟𝑒𝑒𝑒𝑒𝑜𝑜}.

Although microwire array structure will help to increase the solution conductance by decreased ion transfer pathway blockage within the electrolyte due to lower the bubble vol.

fraction, it can cause an increase of dissolved H2 accumulation on some part of the electrode surface compared to the planar electrode under the same nominal current density and therefore lead to an increase in the local reversible hydrogen electrode potential shift.

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Implications for Photoelectrochemical Water Splitting. The Journal of Physical Chemistry C, 2019. 123(1): p. 17-28.

2. Coridan, R.H., et al., Inhibition of Tafel Kinetics for Electrolytic Hydrogen Evolution on Isolated Micron Scale Electrocatalysts on Semiconductor Interfaces.

ACS Appl Mater Interfaces, 2016. 8(37): p. 24612-20.

3. Leistra, J.A. and P.J. Sides, Voltage Components at Gas Evolving Electrodes.

Journal of The Electrochemical Society, 1987. 134(10): p. 2442-2446.

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90: p. 722-737.

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C h a p t e r V I

OPERATIONAL CONSTRAINTS AND STRATEGIES FOR SYSTEMS TO EFFECT THE SUSTAINABLE, SOLAR-DRIVEN REDUCTION OF

ATMOSPHERIC CO

2

6.1 Introduction

A solar-fuels generation system designed to effect the sustainable reduction of CO2

includes components for light absorption and charge separation, electrocatalysis of both the CO2-reduction reaction (CO2RR) and the oxygen-evolution reaction (OER), and a mechanism to transport ions between the two reaction chambers while maintaining robust product separation for both efficiency and safety reasons. Efficient electrochemical or photoelectrochemical conversion of CO2 into usable fuels under mild pressure and temperature conditions entails greater physical and chemical constraints than efficient solar-driven water-splitting systems that can generate renewable H2(g).

At the laboratory scale, no currently known catalyst can perform the multi-electron, multi-proton, electrochemical or photoelectrochemical CO2RR efficiently and selectively.

Polycrystalline metal electrodes are among the most studied class of materials for electrocatalysis of the CO2RR, and most metals have been classified as being selective for CO, HCOO^-, or H2.¹ Copper and copper-containing metal alloys have shown promise for forming hydrocarbons and C-C coupled products with a wide array of major and minor products, albeit at high overpotentials and with limited stability under operating

This chapter is based on results in: Yikai Chen, Nathan S Lewis and Chengxiang Xiang, Energy Environ. Sci., 2015, 8, 3663-3674 – Published by The Royal Society of Chemistry.

conditions.² Recent work on single-crystal,³ nanostructured Au substrates⁴ or oxide- derived Cu substrates⁵ has shown the preferred formation of certain products with limited selectivity and activity. The low activity for the hydrogen-evolution reaction (HER) of semiconductor surfaces may provide opportunities to improve the electrocatalytic performance of GaAs,^6-8 GaP,^{9, 10} InP,^{6, 11} and of other semiconductors for CO2RR.

Assuming the discovery of a suitable catalyst, robust and efficient couplings between the CO2RR, the oxygen-evolution reaction (OER), and the necessary ionic transport processes between two potentially different electrolytes or solvent environments will be required for operation of a full, efficient, sustainable CO2RR system. Traditional three-electrode, two- compartment electrochemical cells are typically employed to study the catalytic and energy-conversion performance of electrocatalysts and semiconductor/catalyst assemblies.¹² However, the transport of ions between the working electrode compartment (cathode chamber) and the counter electrode compartment (anode chamber) is often far from ideal, and the resistive losses and concentration overpotentials are typically compensated for by the additional external bias applied by the potentiostat.¹³ The efficient and sustainable coupling of the CO2RR and OER, with low potential losses and minimal product crossover between the two chambers, has been investigated only to a very limited degree. Moreover, in the absence of perfectly selective catalysts for both the CO2RR and OER, a robust and efficient separator needs to be developed to prevent product crossover and thus provide efficient and safe operation of a CO2RR system. While traditional membrane separators such as Nafion™ ^14-19 are highly conductive and effective for preventing gas crossover in water-splitting systems, Nafion membranes yield high crossover losses in direct methanol fuel cells and would not be suitable for solar-driven CO2RR devices that produce alcohols as products. Development of membranes with the desired permeability and ionic conductivity in the presence of a variety of solution species thus constitutes a significant research opportunity for CO2RR systems.

Regardless of the performance of the full electrochemical cell at the laboratory scale, the sustainable reduction of CO2 at global scale will additionally require effective mass

transport and uptake of atmospheric CO2 on large areas of the Earth’s surface. The large-scale, sustainable reduction of CO2 requires a robust and cost-effective method for the delivery of CO2 to the cathode surface of the device. Whereas liquid water or water vapor is readily able to produce sufficient reactant flux to allow for construction of an efficient solar-driven water-splitting system,²⁰ the low concentration of CO2 in the atmosphere (~400 ppm), and the low solubility of CO2 in aqueous solutions (~34 mM at standard temperature and pressure), present significant physical limitations to obtaining sufficient reactant transport to achieve technologically relevant efficiencies for the operation of a solar-driven CO2RR system with atmospheric CO2. To produce a reasonable partial pressure of CO2 by direct air capture, the surface area for the CO2 collection and concentration is likely to be many orders of magnitude larger than the surface area for the solar photon collection and conversion part of the system. Use of separate CO2

concentration and reduction systems would present additional challenges for integration and coupling of the two technologies. While active research and development has been pursued to achieve efficient capture of CO2 from air,^21-25 significant advances are still needed to make such technologies cost effective and functional in the presence of humidity and temperature variations in the atmosphere.

In this work, we have evaluated analytically the transport limitations of CO2 from the tropopause down to a cathode surface, through five different regions with five different length scales (from tens of nanometers to tens of kilometers) (Figure 6.1a) that are coupled in series from a mass transport perspective. In each case, an effective mass transfer coefficient, σi, has been obtained. The mass transfer coefficients will add reciprocally to produce the reciprocal of the overall CO2 mass transfer coefficient of the system, σsystem:

1

σ𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡𝑜𝑜𝑏𝑏 =∑ _σ¹

𝑜𝑜 𝑖𝑖 (Eq. 6.1) The approach allows estimates of the concentration overpotentials and achievable solar- to-fuels efficiency for a hypothetical CO2 reduction reactor fed by air that contains the same concentration of CO2 as the surrounding atmosphere. We describe and model

Figure 6.1. (a) Schematic illustration of CO2 transport in five different regions with five different length scales. (b) Schematic illustration of the model used for CO2 transport near the cathode surface that contains an aqueous layer with a variety of solution species.

(c) Schematic illustration of the CO2RR reactor that incorporates a light absorber (LA), a catalyst-embedded, thin-layer membrane assembly (orange), an anode compartment for OER (green) and a proton-transport electrolyte (blue).

quantitatively the effects of two strategies to improve the feasibility of producing efficient and sustainable CO2 transport to a cathode surface at p_CO2 = 400 ppm:

development of new catalysts analogous to metalloenzymes such as carbonic anhydrase, to dramatically enhance the kinetics of the interconversion of bicarbonate ions and CO2 in the bicarbonate buffer system and thus improve the ability to maintain the concentration of CO2 in the aqueous solution at p_CO2= 400 ppm; and the use of a thin-layer cell architecture that minimizes the required CO2 transport in an aqueous or polymeric electrolyte. These two strategies could, in principle, yield significant increases in the air/electrolyte CO2

conductance relative to the natural transport at global scale of CO2 across the atmosphere/ocean interface. The atmospheric transport of CO2 between the troposphere and atmospheric boundary layer (ABL), and the corresponding constraints for the transport of CO2 to the reactor at regional scale, have also been evaluated to complete the expression for the overall system CO2 conductance and in turn to establish the ultimate limit on the efficiency of a sustainable solar-driven CO2RR system deployed at global scale.

6.2 Modeling

6.2.1 CO2 transport

Figure 6.1a shows a schematic illustration of the CO2 transport from tropopause towards the surface of a CO2RR device. Five different layers with different characteristic length scales are coupled in series with the same CO2 flux. Three distinctive types of phase boundaries: gas/gas (troposphere/atmospheric boundary layer (ABL), ABL/canopy layer), gas/electrolyte (canopy layer/membrane layer, or canopy layer/liquid layer) and electrolyte/electrode interface (liquid layer/cathode surface, or membrane layer/cathode surface) were included in the transport schematics. The CO2 concentrations within the troposphere, the ABL, and the canopy layer were assumed to separately be constant due to rapid turbulent mixing within each layer, while the net CO2 flux across the troposphere/ABL interface and across the ABL/canopy interface results in CO2

concentration differentials between the different gas-phase layers. The equilibrium CO2

concentrations at the various gas/electrolyte interfaces were assumed to follow Henry’s

law. At the electrolyte/electrode interfaces, and a 4-electron/4-proton OER was assumed and a 6-electron/6-proton CO2RR was assumed, to represent a favorable situation for the ratio of CO2 molecules to electrons in the electrochemical cell.

At the phase boundaries, the CO2 flux across the interface, ΦCO2 [mol cm^-2 s^-1] was expressed as ΦCO2= σ ΔC, where σ is an effective mass transfer coefficient [cm s^-1] and ΔC is the concentration differential of CO2 [mM] between the two neighboring layers. Two transport pathways, one containing the membrane layer (σ1, σ2, σ4 and σ6) and the other containing the liquid layer (σ1, σ2, σ3 and σ5), were modeled and evaluated in this study.

The CO2 flux across all of the interfaces, ΦCO2, can be expressed as ΦCO2= σsystem

(Ctroposphere-Ccathode), where σsystem is the overall effective mass transfer coefficient of the system, which can be expressed as ¹

σ𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡𝑜𝑜𝑏𝑏= _σ¹

1+_σ¹

2+_σ¹

3+_σ¹

5 for the system that contains the liquid layer and as ¹

σ𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡𝑜𝑜𝑏𝑏= _σ¹

1+_σ¹

2+_σ¹

4+_σ¹

6 for the system that contains the membrane layer. As a result of the reciprocal summation relation, the overall effective mass transfer coefficient of the system, σsystem, is smaller than any individual mass transfer coefficient, and is dominated by the process with the smallest mass transfer coefficient in the system.

6.2.2 One-dimensional traditional cell design

Figure 6.1b illustrates the one-dimensional (1-D) model used in this work to evaluate the CO2 transport near a cathode performing a 6-electron/6-proton CO2RR. The electrode was assumed to have a sufficiently high catalytic activity that under operating conditions the CO2 concentration was driven to zero at the electrode surface. A well-mixed bulk solution was assumed, and two hydrodynamic boundary layers (HBL), that accounted for forced convective mixing (lHBL = 10 μm) and natural convection (lHBL = 100 μm), respectively, were introduced near the cathode surface. Rapid equilibration of CO2 was assumed at the air-electrolyte interface, and the acid-base equilibria for the carbonate buffer and for the phosphate buffer, as well as the equilibria for the corresponding chemical reactions, were included in the model for the liquid regions. The same configuration,

representing a well-mixed bulk solution layer and two HBLs, was assumed for the OER at the anode.

Figure 6.1 summarizes the diffusion coefficients of species in water, as well as the forward and reverse rate constants for the bicarbonate buffer solution, that were used in the simulation.^{26, 27} Note that the total CO2 concentrationin Figure 6.1 has been defined as the sum of the dissolved CO2 in aqueous solution, CO2(aq), and the carbonic acid concentration, H2CO3. The forward and reverse reaction rates, k1+ and k1-, respectively, fully describe the acid-base equilibrium between CO2(aq), H2CO3 and HCO3- in the buffer system.^{26, 27} The transport loss in the system was assumed to be independent of the detailed electrocatalytic parameters for the cathode and anode, and was assumed to be a function only of the operating current density at the electrode surfaces. In some situations, an interconversion enhancement factor was introduced to increase both the forward and reverse reactions for reaction (1-4) in Figure 6.1, to represent the behavior of a hypothetical catalyst for these reactions with the catalyst having a reactivity analogous to that exhibited by the enzyme carbonic anhydrase.

6.2.3 Catalyst-embedded, thin-layer membrane assembly for rapid transport of CO2

Figure 6.1c illustrates a conceptually distinct system that consists of a CO2-reduction reactor based on a catalyst-embedded, thin-layer membrane device architecture. The cell consists of a solar-driven CO2RR reactor that incorporates a light absorber (LA), a catalyst- embedded thin-layer membrane assembly, an anode compartment, and an electrolyte that is either buffered at near-neutral pH or is maintained under alkaline conditions. The LA (red) captures the solar photons and converts them into energetic electrons and holes for the fuel-forming reactions. The device has been designed to achieve large mass transport fluxes of CO2 to the electrode surface, based purely on diffusional transport of CO2 in the ultrathin electrolyte, because the catalyst-embedded, thin-layer membrane assembly (orange) reduces the length of the pathways for the CO2 transport within the polymer electrolyte.

In this device, the equilibrium CO2 concentration at the gas/polymer electrolyte interface was assumed to follow Henry’s law. Three different permeabilities for CO2

transport in the polymer electrolyte were assumed. The buffered near-neutral pH or alkaline electrolytes (blue) were chosen so that the small proton concentration at the cathode surface would suppress the rate of the hydrogen-evolution reaction (HER) relative to the rate of the CO2RR. The anode compartment (green) performed the OER and provided the necessary proton source for the cathode. The anode compartment also contained an anion-exchange membrane for the alkaline operation or a bi-polar membrane for CO2RR and OER at two different pHs, to facilitate the ionic transport and reduce the product crossover in the system.

6.2.4 Governing equations

Ionic species and neutral species in the electrolyte solution were modeled using the Nernst-Planck equation,¹² in which the diffusion, migration and bulk reactions of water and buffer dissociation were explicitly included. Forced convection was approximated by the use of the hydrodynamic boundary layers.

The total voltage requirement for the electrochemical cell was calculated as the sum of the equilibrium potential , kinetic overpotentials , solution potential drop losses , and the Nernstian potential losses associated with pH gradients,

, as well as the potential drops associated with CO2 concentration gradients, at the surface of the electrodes:

(Eq. 6.2)

(

∆φcell

)

( )

E0

( )

^η

(

∆φsolution

)